$g(t) = -2t+5(h(t))$ $h(t) = 6t^{2}+5t$ $ h(g(-1)) = {?} $
Answer: First, let's solve for the value of the inner function, $g(-1)$ . Then we'll know what to plug into the outer function. $g(-1) = (-2)(-1)+5(h(-1))$ To solve for the value of $g$ , we need to solve for the value of $h(-1)$ $h(-1) = 6(-1)^{2}+(5)(-1)$ $h(-1) = 1$ That means $g(-1) = (-2)(-1)+(5)(1)$ $g(-1) = 7$ Now we know that $g(-1) = 7$ . Let's solve for $h(g(-1))$ , which is $h(7)$ $h(7) = 6(7^{2})+(5)(7)$ $h(7) = 329$